Squeeze $3, cbet 50% pot. Reason for bigger sizing pre is that we don't want more than one caller oop (and preferably no callers). The smaller cbet enables us to still get stacks in comfortably if we want to (much like a 3bet pot) and yet saves us some money when we need to fold (like we do in this hand).

Whether the squeeze is profitable is difficult to say. It certainly can be in the right circumstances and it would be a good exercise for you to work through some EV calculations, including how often your cbet would need to get through to make this profitable.

Re range - expect 22/18 villain to flat with TT-QQ, AQ, AK, maybe more pocket pairs if he's confident btn will come along and perceives hero or btn to be fishy or fit or fold. AA and KK would be a 4bet with btn still to act.